BACKGROUND OF THE INVENTION

[0001]
The present invention relates to a multicarrier communication system and a receiver thereof, and more particularly to a multicarrier communication system using the interference between a target subchannel and two or more upper and lower subchannels (ICI) and a receiver thereof.

[0002]
The bit error rate (BER) of the multicarrier communication system in filter bank modulation, DMT modulation and FMT modulation can be improved by using receive signals that include distortion by interchannel interference (ICI). Interchannel interference occurs by the malfunction of a system in communication systems, such as OFDMCDMA, or due to an unavoidable environment such as the loss of orthogonality between subchannels. Interchannel interference, which is called the “leak of spectrum energy”, at times the crosstalk between subchannels, is caused by a leak.

[0003]
A major advantage of the turbo receiver of the present invention is that the phenomenon of ICI is handled as a zero mean Gaussian distribution random variable (e.g. Gaussian approximation used in the following document 1 below), for which a finite state discrete Markov process model is used. For such an ICI model, simple Gaussian approximation seems to be more practical because of the nature of ICI. The turbo receiver of the present invention is based on a maximum posterior probability estimation algorithm. In this turbo receiver, information derived from one subchannel after nonlinear processing refines the estimated maximum posterior probability of the latter channel, and in the same way, the information derived from the other subchannel refines the estimated maximum probability of the former subchannel.

[0004]
Document 1: K. Sathanathan and C. Tellambura: “Probability of error calculation of OFDM system with frequency offset”, IEEE Trans. Commun., Vol. 49, NO. 11, November 2001, pp. 18841888.

[0005]
(a) Relationship Between Frequency Offset and ICI

[0006]
In the case of a multicarrier communication system where a band is divided into a plurality of subbands, which are independent narrow bands, and the transmission data of each subband is frequencymultiplexed and transmitted and received, the selection of a filter set in a multicarrier communication system for filter bank modulation, DMT (Discrete Multitone) modulation and FMT (Filtered Multitone) modulation, has been executed under the constraint that intersymbol interference (ISI) and interchannel interference (ICI) are completely removed.

[0007]
In an ideal transmission channel where there is no Doppler shift and where there is no offset frequency between transmitter/receiver and signal distortion does not occur, this constraint guarantees the receiver that the recovery of transmission symbols to be error free. However the frequency offset which is generated in each channel, due to inaccurate tuning of the oscillator and the Doppler shift, causes BER deterioration due to a spectrum leak or ICI.

[0008]
The only method to relax such deterioration of BER is to minimize the frequency offset, and more particularly, to maintain it to be within 1% of the subcarrier frequency interval. This method, however, requires accurate frequency offset estimation, and also if the noise level is high when multicarrier signals mixed with noise are received, the accuracy of frequency offset estimation is affected. Also according to this method, the Doppler shift is not consistent with respect to the transmission symbols in a highspeed fading channel, and operation becomes inaccurate in a highspeed fading channel which changes depending on the time.

[0009]
Here the case of a DMT base system and an ideal white Gaussian noise (AWGN) channel is assumed. It is also assumed that the level of intersymbol interference ISI can be ignored compared with the interchannel interference ICI and other noise signals. To simplify description, only a target channel, the first adjacent subchannel located below the target subchannel and the second adjacent subchannel located above the target subchannel, are considered. FIG. 1 and FIG. 2 show the frequency response of the three channels in the case when the frequency offset is zero (FIG. 1), and in the case when the frequency offset is not zero (FIG. 2). The signals of the central frequencies f_{1}, f_{2 }and f_{3 }corresponding to the first, second and third subchannels are indicated by the vertical arrows in FIG. 1 and FIG. 2. In FIG. 1 and FIG. 2, the subchannel number 0 (ch0) indicates the target subchannel, the subchannel number −1 (ch−1) is a subchannel located below the target subchannel in the frequency scale, and the subchannel number +1 (ch+1) indicates the subchannel located above the target subchannel in the frequency scale. If the cycle of the DMT symbol is T, then the frequency scale is normalized with a channel interval equal to 1/T. In other words, one unit of the frequency scale is the channel interval. As FIG. 1 shows, when the frequency offset (normalized by the channel interval) α is 0, the transfer function of the lower subchannel and the upper subchannel, indicated by the solid line A and the dotted line B in FIG. 1, gives infinite attenuation in the central frequency f_{2 }of the target subchannel (dotted line C). In the same way, the transfer function of the target subchannel gives infinite attenuation in the central frequencies f_{1 }and f_{3 }of the lower and the upper subchannels. In other words, if the frequency offset α is zero, ICI is not generated between adjacent subchannels. This means that if the frequency offset is zero, the respective subchannels intersect orthogonally, and ICI does not exist at all.

[0010]
If the frequency offset a is not zero, however, the orthogonality of the subchannels is affected, and ICI is generated. FIG. 2 shows the spectrum characteristics of each subchannel of the DMT system when the frequency offset α is not zero. The spectrum of adjacent channels cross at −3 dB, and the first sidelobe is −13 dB, which is high. In order to avoid a complex system model, the case when the subchannels which are distant for a 1 or 2 channel interval interfere with each other will be considered below. It is clear that the spectrum of an adjacent subchannel has a mutual gain which is not zero, which is indicated as α_{01}, α_{11}, α_{10}, α_{−10}, α_{01 }and α_{−11}. In these notations the first index of a indicates the interference source subchannel, and the second index indicates the interference target subchannel. In other words, α_{−10 }indicates the leak transfer coefficient (amplitude) from the lower subchannel with the subchannel number −1 to the target channel with the subchannel number 0. α_{−11 }indicates the leak transfer coefficient (amplitude) from the lower subchannel with the subchannel number −1 to the upper subchannel with the subchannel number 1, α_{01 }indicates the leak transfer coefficient from the target subchannel with the subchannel number 0 to the higher subchannel with the subchannel number 1, α_{01 }indicates the leak transfer coefficient from the target subchannel with the subchannel number 0 to the lower subchannel with the subchannel number −1, and α_{10}, indicates the leak transfer coefficient from the higher subchannel with the subchannel number +1 to the target subchannel with the subchannel number 0. As described above, if the frequency offset α is not zero, the mutual gain which is not zero, that is ICI (crosstalk), is generated between subchannels.

[0000]
(b) General Model of Communication System

[0011]
FIG. 3 is a general model (four subchannel model) depicting the mutual ICI of four subchannels in a DMT system having frequency offset. Compared with the three subchannel model (see FIG. 4), according to the turbo receiver of the present invention, the four subchannel model can improve the total system BER in more cases because of the low roll off spectrum characteristics of DMT. 1 _{1}, 1 _{2}, 1 _{3 }and 1 _{4 }are the transmitters of the subchannels ch−1, ch0, ch+1 and ch+2, 2 _{1}, 2 _{2}, 2 _{3 }and 2 _{4 }are the receivers of each subchannel, 3 _{1}, 3 _{2}, 3 _{3 }and 3 _{4 }are the transmission lines of each subchannel. 4 _{ij }is a multiplier to multiply the subchannel signal D_{i }by the leak transfer coefficient (interference coefficient) α_{ij }of the subchannel with the number i to the subchannel with the number j respectively, 5 _{1}, 5 _{2}, 5 _{3 }and 5 _{4 }are the first synthesizing units for synthesizing the crosstalk (ICI) from the adjacent subchannel to its own subchannel signal, 6 _{1}, 6 _{2}, 6 _{3 }and 6 _{4 }are the second synthesizing units for synthesizing the crosstalk (ICI) from the subchannel which is distant from two channel intervals to its own subchannel signal, and 7 _{1}, 7 _{3}, 7 _{3 }and 7_{4 }are the noise synthesizing units.

[0012]
As FIG. 3 shows, the signals from the lower subchannel ch−1 leak into the target subchannel ch0 via the crosstalk coefficient α_{−10}, the signals from the upper subchannel ch+1 leak into the target subchannel via the crosstalk coefficient α_{10}, and the signals from the upper subchannel ch+2 leak into the target subchannel ch0 via the crosstalk coefficient α_{20}. Also the signals from the lower subchannel ch−2 leak into the target subchannel via the crosstalk coefficient α_{−20}, but description thereof will be omitted since this can be regarded as the same as the leak from the ch+2. In the model in FIG. 3, the subchannels that cause mutual interference are limited to the upper and lower subchannels, but the number of subchannels in the entire communication system is not limited, so the model in FIG. 3 can also be applied to a multicarrier communication system that has N number of subchannels, where N is 4 or a greater number. In such a case as well, interference to each subchannel is only from the lower two subchannels and the upper two subchannels. In this case, the interference coefficient indicates a chain of coefficients. The noise components denoted as n_{1}(t), n_{2}(t), n_{3}(t) and n_{4}(t) in FIG. 3 are statistically independent (no correlation) because of the frequency orthogonality between the subchannels.

[0013]
The subchannels are located in the frequency domain, but this model can be applied not only to a DMT modulation type or a filter bank modulation type system, but also to other systems. The dimensions can be expanded to other domains, such as space (space division multiplex axis) and polarity.

[0000]
(c) Technical Problem

[0014]
The model in FIG. 3 is beneficial in terms of understanding the physical process which causes ICI. The problem of this model lies in accurately deciding the receive signals of each subchannel and the value of the transmission information symbols (a sign if a binary number).

[0015]
One possible method to reduce ICI in a receiver is applying the decision feedback equalizer (DFE) to cancel ICI, which is proposed in the following document 2. Document 2: Viterbo and K. Fazel, “How to combat long echoes in QFDM transmission schemes: Subchannel equalization or more powerful channel coding,” Proc. IEEE Globecom '95, Singapore, November 1995, pp. 20692074.

[0016]
If the output of an individual receiver is in hard bit decision (hard decision) format, then sharing information among subchannels has only a few benefits. This restricts the operation range of DFE which uses a hard decision.

[0017]
The above mentioned approach is effective in many practical cases, but is for minimizing the effect of ICI, and is the second best approach. Since ICI includes information on transmission symbols, it is possible to remodulate the receive signals quite well by using this transmission symbol information included in ICI.
SUMMARY OF THE INVENTION

[0018]
With the foregoing in view, it is an object of the present invention to improve BER performance using the ICI in a communication system where ICI exists.

[0019]
It is another object of the present invention to decrease BER based on the posterior probability using ICI.

[0020]
The present invention is a multicarrier communication system for transmitting/receiving signals via at least four subchannels, comprising a transmitter for transmitting data independently via four channels, a receiver comprising a receive unit disposed for each subchannel for receiving data from a corresponding subchannel and performing soft decision of the receive data, and means for inputting soft decision target values in the receive units corresponding to subchannels other than a target subchannel to a receive unit of the target subchannel, wherein the receive unit of the target subchannel adjusts its own soft decision target value using the soft decision target values that are input from the receive units of the other subchannels, and decides the receive data based on the adjusted soft decision target value.

[0021]
The receive unit of the target subchannel further comprises means for computing a difference between a probability that the data received from the target subchannel is one value of a binary and a probability that the data is the other value of a binary as the soft decision target value, considering degree of coupling of crosstalk paths, means for adjusting the soft decision target value of the target subchannel using the soft decision target values that are input from the receive units of the other subchannels, and a decision unit for deciding the receive data based on adjusted the soft decision target value.
BRIEF DESCRIPTION OF THE DRAWINGS

[0022]
FIG. 1 shows the frequency characteristics when the frequency offset is zero;

[0023]
FIG. 2 shows the frequency characteristics when the frequency offset is not zero;

[0024]
FIG. 3 shows a general model for depicting the mutual ICI of four channels in a DMT system having frequency offset;

[0025]
FIG. 4 is a general block diagram depicting a communication system that demodulates receive data using the interference between lower one subchannel and upper one subchannel;

[0026]
FIG. 5 is a block diagram depicting a receiver of a three subchannel model;

[0027]
FIG. 6 is a general block diagram depicting a communication system for demodulating receive data using the interference between lower one subchannel and upper two subchannels, which shows the case where the number of subchannels is 4 (four subchannel model);

[0028]
FIG. 7 is a first block diagram depicting a receiver in the case when the crosstalk from upper two subchannels and lower one subchannel exist, and indicates the configuration of the left side of the receiver;

[0029]
FIG. 8 is a second block diagram depicting a receiver in the case when the crosstalk from upper two subchannels and lower one subchannel exist, and indicates the configuration of the right side of the receiver;

[0030]
FIG. 9 is a diagram depicting the constellation of the target subchannel according to the number of repeats according to the turbo receiver of the present invention;

[0031]
FIG. 10 is a characteristic diagram depicting the average BER performance of the turbo receiver of the present invention and a conventional matched filter base receiver;

[0032]
FIG. 11 is a block diagram depicting a DMT base communication system using the turbo receiver of the present invention; and

[0033]
FIG. 12 is a characteristic diagram depicting the BER performance of the DMT receiver having the turbo processing function of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0034]
(A) General Configuration of Communication System in the Case of Three SubChannels

[0035]
FIG. 4 is a general block diagram depicting a communication system that demodulates receive data using the interference between a total of two subchannels, lower and upper, and is a case when the number of subchannels is three. The intent of the present invention is to provide a communication system having at least four subchannels (four subchannel model), but a communication system having three subchannels (three subchannel model) will be described first to assist in understanding the present invention.

[0036]
The communication system in FIG. 4 comprises three transmitters, 21, 22 and 23, for transmitting data independently via the three subchannels, ch−1, ch0 and ch+1 respectively, many crosstalk paths 31 _{ij }having a coupling coefficient α_{ij }to the ith to the jth subchannel, three receivers, 40, 50 and 60, which are installed for each subchannel for receiving data from the corresponding subchannel and performing the soft decision of the receive data, and means 71 and 72 for inputting the soft decision target value of each receiver to another receiver. 3234 and 3537 are synthesizing units for synthesizing ICI signals and noise.

[0037]
The receiver 50 of the subchannel ch0 adjusts its own soft decision target value using the soft decision target values which were input from the receivers 40 and 60 of the lower and upper subchannels ch−1 and ch+1, and decides “0” or “1” of the receive data based on the soft decision target value. In the same way, the other respective receivers adjust its own soft decision target value using the soft decision target values which were input from the receivers of the lower and upper subchannels, and decides “0” or “1” of the receiver data based on the soft bit decision target value.

[0000]
(B) Algorithm of Receive Symbol Demodulation in Three SubChannels

[0038]
An algorithm for the receiver of the target subchannel ch0 to demodulate the receive signals in the communication system shown in FIG. 4, will be described.

[0039]
The principle of the demodulation algorithm is to derive the value InD_{0 }which indicates the difference of the posterior probability P(D_{0}=+1/y(t)) of the information symbol received by the target subchannel ch0 becoming “0” (=+1) and the posterior probability P(D_{0}=−1/y(t)) of this becoming “1” (=−1). This is because if the difference InD_{0 }of the posterior probability can be derived, it can be decided whether the receive information symbol is “0” or “1”. In other words, the probability difference InD_{0 }of the target subchannel is the difference between the posterior probability P(D_{0}=+1/y(t)) of the receive information symbol becoming “0” (=+1), and the posterior probability P(D_{0}=−1/y (t)) of this becoming “1” (=−1), so if InD_{0}>0, then the receive information of the target subchannel is “0”, and if InD_{0}<0, then the receive information of the target subchannel is decided as “1”. According to the above, the value InD_{0 }to indicate the difference of the posterior possibility, is derived.

[0040]
It is assumed that the binary information is transmitted as the signal S*_{ij}(t) via the two adjacent subchannels. The index i of S*_{ij}(t) is determined by the sign of the information symbol D_{i}(i=−1, 0 or 1) in subchannel i. In other words,
if D_{i}=+1, then j=0 if D_{i}=−1, then j=1 (1)
Hereafter to simplify notation, the time dependency of S*_{ij}(t) in expressions is omitted. In other words, S*_{ij}(t) is denoted as S*_{ij}.

[0041]
It is assumed that the transmission information symbol D_{i }is statistically independent (no correlation) and is an equally distributed probability variable. As FIG. 4 shows, the signal of the target subchannel affected by ICI from the lower and upper subchannels is expressed as the linear coupling of the signals S*_{−1j }and S*_{1j }transmitted by the upper and lower subchannels and the target channel signal S*_{0j }by the crosstalk coefficient α. The crosstalk coefficient α is a value according to the leak of crosstalk. If the information symbol D_{0 }of the target channel is +1, then the receive signal S_{j }(j=0−3) of the target channel becomes
$\begin{array}{cc}\{\begin{array}{c}{S}_{0}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=+1\\ {S}_{1}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=1\\ {S}_{2}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=+1\\ {S}_{3}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=1\end{array}& \left(2\right)\end{array}$
depending on whether the signals D_{−1 }and D_{1 }of the lower and upper subchannels are +1 or −1. j of the signal S_{j }indicates the signal number. In the same way, if the information symbol D_{0 }of the target channel is −1, then the receive signal S_{j }(j=4−7) of the target channel becomes
$\begin{array}{cc}\{\begin{array}{c}{S}_{4}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{3},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=+1\\ {S}_{5}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{2},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=1\\ {S}_{6}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{1},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=+1\\ {S}_{7}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{0},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=1\end{array}& \left(3\right)\end{array}$
depending on whether the signals D_{−1}, and D_{1 }of the lower and upper subchannels are +1 or −1.

[0042]
After introducing ICI, S_{j }(j=0, 1, 2, . . . 7) is used as eight signals in the input of the receiver of each subchannel. The index j of S_{j }in the expressions (2) and (3) indicates the signal number, and is determined by airing the symbols D_{−1}, D_{1 }and D_{0 }in the lower subchannel, upper subchannel and target subchannel.

[0043]
By considering the following [1] and [2], an algorithm for optimum reception can be further developed. In other words, by considering [1] that the signs of some information signals are the opposite, that is −S*
_{−10}=−S*
_{−11}, S*
_{00}=−S*
_{01}, and S*
_{10}=−S*
_{11}, and [2] to transmit information symbols a same signal is used for the lower and upper subchannels and target subchannel, that is S*
_{−10}=S*
_{00}=S*
_{10}, and S*
_{−11}=S*
_{01}=S*
_{11}, the algorithm for optimum reception can be further developed. The latter [2] indicates that all the subchannels have the same value and the information signals of all the subchannels have no difference in amplitude, waveform and energy. In this case the signals of the expressions (2) and (3) in each subchannel become a pair, having opposite signs, as shown in the following expressions.
$\begin{array}{cc}\{\begin{array}{c}{S}_{0}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{7}\\ {S}_{1}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{6}\\ {S}_{2}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{5}\\ {S}_{3}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}={S}_{4}\end{array}& \left(4\right)\end{array}$
From the expression (2), (3) and (4), the posterior probability to receive the signal S
_{j}, that is the posterior probability P(S
_{j}/y (t)) of the receive signal becoming S
_{j}, is given by the following expression.
$\begin{array}{cc}P\left[{S}_{j}/y\left(t\right)\right]={k}_{0}\xb7{P}_{\mathrm{apr}}\left({S}_{j}\right)\xb7P\left(y\left(t\right)/{S}_{j}\right)={k}_{0}\xb7{P}_{\mathrm{apr}}\left({S}_{j}\right)\xb7\mathrm{exp}\left\{\frac{1}{{N}_{0}}{\int}_{0}^{T}{\left[y\left(t\right){S}_{j}\right]}^{2}\text{\hspace{1em}}dt\right\}& \left(5\right)\end{array}$
where

 k_{0 }is a normalized factor
 j is a signal number (j=0, 1, . . . 7),
 y(t) is a synthesized signal (y(t)=S_{j}+n(t)) of the signal series S_{j }involving ICI and the white Gaussian noise n(t) having the spectrum power intensity N_{0},
 P_{apr}(S_{j}) is a prior probability of the receive signal S_{j}, and
 P(y(t)/S_{j}) is a conditional probability, and is a probability where the transmitted sign signal is S_{j }when the receive signal is y(t).

[0049]
In the prior probability P_{apr}(S_{j}) (j=0, 1, . . . 7) is expressed as a crossproduct of the prior probability of the signal of the target subchannel becoming S*_{00 }or S*_{01 }and the posterior probability of the information signal S*_{ij }in the two adjacent subchannels. In other words, if D_{0}=+1, the prior probability P_{apr}(S_{j}) becomes
$\begin{array}{cc}\{\begin{array}{c}{P}_{\mathrm{apr}}\left({S}_{0}\right)=P\left({S}_{10}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{10}^{*}\right)\\ {P}_{\mathrm{apr}}\left({S}_{1}\right)=P\left({S}_{10}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{11}^{*}\right)\\ {P}_{\mathrm{apr}}\left({S}_{2}\right)=P\left({S}_{11}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{10}^{*}\right)\\ {P}_{\mathrm{apr}}\left({S}_{3}\right)=P\left({S}_{11}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{11}^{*}\right)\end{array}& \left(6\right)\end{array}$
and if D_{0}=−1, the prior probability P_{apr}(S_{j}) becomes
$\begin{array}{cc}\{\begin{array}{c}{P}_{\mathrm{apr}}\left({S}_{4}\right)=P\left({S}_{10}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{10}^{*}\right)\\ {P}_{\mathrm{apr}}\left({S}_{5}\right)=P\left({S}_{10}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{11}^{*}\right)\\ {P}_{\mathrm{apr}}\left({S}_{6}\right)=P\left({S}_{11}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{10}^{*}\right)\\ {P}_{\mathrm{apr}}\left({S}_{7}\right)=P\left({S}_{11}^{*}\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{11}^{*}\right)\end{array}& \left(7\right)\end{array}$

[0050]
In expressions (6)(7), P_{apr}(S_{j}) is a prior probability (transmission probability) of the information signal S_{j }with the number j in the target subchannel being transmitted. Prior probability P_{apr}(S*_{ij}) depends on the statistics of the data generation source, and in practical terms it is assumed to be equal to {fraction (1/2)}. Probability P(S*_{ij}) is the posterior probability of the receive signal S*_{ij}, which is different from the prior probability P_{apr}(S*_{ij}), and can be estimated at the receive side with high reliability, so P(S*_{ij})=P(S*_{ij}/y(t)). This is the best estimate of P(S*_{ij}) in the white Gaussian noise channel. And based on this assumption, the expressions (6) and (7) can be rewritten as
$\begin{array}{cc}\{\begin{array}{c}{P}_{\mathrm{apr}}\left({S}_{0}\right)=P\left({S}_{10}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{10}^{*}/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{1}\right)=P\left({S}_{10}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{11}^{*}/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{2}\right)=P\left({S}_{11}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{10}^{*}/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{3}\right)=P\left({S}_{11}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{11}^{*}/y\left(t\right)\right)\end{array}& \left(8\right)\end{array}$
$\begin{array}{cc}\{\begin{array}{c}{P}_{\mathrm{apr}}\left({S}_{4}\right)=P\left({S}_{10}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{10}^{*}/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{5}\right)=P\left({S}_{10}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{11}^{*}/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{6}\right)=P\left({S}_{11}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{10}^{*}/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{7}\right)=P\left({S}_{11}^{*}/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({S}_{11}^{*}/y\left(t\right)\right)\end{array}& \left(9\right)\end{array}$
or when a different relationship exists between the information signal S*_{ij }and the transmission information signal D_{i }(see expression (1)), a substitution of P(S*_{ij})=P(D_{i}=i/y(t)) is possible in expression (6) and (7), and expressions (6) and (7) can be expressed by the following expressions. Here P(S*_{ij}) is a probability of the ith subchannel Di becoming j
$\begin{array}{cc}\{\begin{array}{c}{P}_{\mathrm{apr}}\left({S}_{0}\right)=P\left({D}_{1}=+1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{1}=+1/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{1}\right)=P\left({D}_{1}=+1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({D}_{1}=1/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{2}\right)=P\left({D}_{1}=1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({S}_{1}=+1/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{3}\right)=P\left({D}_{1}=1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({D}_{1}=1/y\left(t\right)\right)\end{array}& \left(10\right)\end{array}$
$\begin{array}{cc}\{\begin{array}{c}{P}_{\mathrm{apr}}\left({S}_{4}\right)=P\left({D}_{1}=+1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=+1/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{5}\right)=P\left({D}_{1}=+1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=1/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{6}\right)=P\left({D}_{1}=1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=+1/y\left(t\right)\right)\\ {P}_{\mathrm{apr}}\left({S}_{7}\right)=P\left({D}_{1}=1/y\left(t\right)\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=1/y\left(t\right)\right)\end{array}& \left(11\right)\end{array}$

[0051]
In the expressions (10) and (11) the prior probability P_{apr}(S_{j})(j=0, 1, 2, . . . 7) of the receive signal S_{j }in the target subchannel is expressed by the crosschannel product of the prior transmission probability P_{apr}(S*_{ij}) of the information signal S*_{ij}, and the posterior probability of the information symbol D_{i }received by the lower and upper adjacent channels being +1 or −1.

[0052]
In the turbo receiver (maximum likely receiver) of the present invention, the sign of the receive information symbol D_{0 }of the target subchannel is determined as follows. That is, the probability of the receive information symbol D_{0 }of the target subchannel (number 0) being +1, which is P(D_{0}=+1/y(t)) and the probability of D_{0 }being −1, which is P(D_{0}=−1/y(t)) are determined respectively, and the sign of the receive information symbol D_{0 }is determined by comparing the values thereof, or comparing the difference of the logarithm thereof and the threshold value.

[0053]
The posterior probability P(D_{0}=j/y(t)) of the receive information symbol D_{0 }of the target subchannel being j can be acquired as the posterior probability of the signals of which D_{0 }is j being received. Therefore the posterior probability P(D_{0}=+1/y(t)) is a probability of the receive information signal D_{0 }of the target subchannel becoming “0” (=+1) can be determined as follows. That is, the signal to transmit the information symbol of “0” (=+1) in the target subchannel is S_{0}S_{3 }according to the expressions (1) and (2), so the posterior probability P(D_{0}=+1/y(t)) of the receive information symbol D_{0 }of the target subchannel becoming “0” (=+1) becomes the sum of the posterior probability to receive the signals S_{0}S_{3}, which can be determined by the expression (12a). In the same way, the posterior probability P(D_{0}=−1/y(t)) of the receive information symbol D_{0 }of the target subchannel becoming “0” (=−1) can be determined by the expression
$\{\begin{array}{cc}P\left({D}_{0}=+1/y\left(t\right)\right)=k\xb7[P\left({S}_{0}/y\left(t\right)\right)+P\left({S}_{1}/y\left(t\right)\right)+P\left({S}_{2}/y\left(t\right)\right)+P\left({S}_{3}/y\left(t\right)\right]& \left(12a\right)\\ P\left({D}_{0}=1/y\left(t\right)\right)=k\xb7\left[P\left({S}_{4}/y\left(t\right)\right)+P\left({S}_{5}/y\left(t\right)\right)+P\left({S}_{6}/y\left(t\right)\right)+P\left({S}_{7}/y\left(t\right)\right)\right]& \left(12b\right)\end{array}$
If the expression (5) is applied to (12a) (where k_{0}=1), the expression (13) is established,
P(D _{0}=+1/y(t))=k·[P _{apr}(S _{0})·P(y(t)/S _{0})+P _{apr}(S _{1})·P(y(t)/S _{1})+k·[P _{apr}(S _{2})·P(y(t)/S _{2})+P _{apr}(S _{3})·P(y(t)/S _{3})] (13)
and if the expression (5) is applied to (12b) (where k_{0}=1), the expression (14) is established.
P(D _{0}=−1y(t))=k·[P _{apr}(S _{4})·P(y(t)/S _{4})+P _{apr}(S _{5})·P(y(t)/S _{5})+k·[P _{apr}(S _{6})P(y(t)/S _{6})+P _{apr}(S _{7})·P(y(t)/S _{7})] (14)

[0054]
If the expressions (10) and (11) are substituted for the expressions (13) and (14) and y(t) of P(D_{i}=±1/y(t)) is omitted for simplification (that is P(D_{i}=±1/y(t))=P(D_{i}=±1)), then the expressions (15) and (16) are acquired.
$\begin{array}{cc}P\left({D}_{0}=+1/y\left(t\right)\right)=k\xb7\left[\begin{array}{c}P\left({D}_{1}=+1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{0}\right)+\\ P\left({D}_{1}=+1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{1}\right)+\\ P\left({D}_{1}=1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{2}\right)+\\ P\left({D}_{1}=1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)\xb7P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{3}\right)\end{array}\right]& \left(15\right)\end{array}$
$\begin{array}{cc}P\left({D}_{0}=1/y\left(t\right)\right)=k\xb7\left[\begin{array}{c}P\left({D}_{1}=+1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{4}\right)+\\ P\left({D}_{1}=+1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{5}\right)+\\ P\left({D}_{1}=1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{6}\right)+\\ P\left({D}_{1}=1\right)\xb7{P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)\xb7P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{7}\right)\end{array}\right]& \left(16\right)\end{array}$
Then the expression (15) is further transformed, and the expressions (17a) and (17b) are acquired.
P(D _{0}=+1/y(t))=k·P _{apr}(S _{00} ^{*})·[P(D _{−1}=+1)·P(D _{1}=+1)·P(y(t)/S _{0})+P(D _{−1}=+1)·P(D _{1}=−1)·P(y(t)/S _{1})]+k·P _{apr}(S _{00} ^{*})·[P(D _{−1}=−1)·P(D _{1}=+1)·P(y(t)/S _{2})+P(D _{−1}=−1)·P(D _{1}=−1)·P(y(t)/S _{3})] (17a)
P(D _{0}=+1/y(t))=k·P _{apr}(S _{00} ^{*})·[P(D _{−1}=+1)·{P(D _{1}=+1)·P(y(t)/S _{0})+P(D _{1}=−1)·P(y(t)/S)}]+k·P _{apr}(S _{00} ^{*})·[P(D _{−1}=−1)·{P(D _{1}=+1)·P(y(t)/S _{2})+P(D _{1}=−1)·P(y(t)/S _{3})}] (17b)
In the same way, the expression (16) is transformed, and the expressions (18a) and (18b) are acquired.
P(D _{0}=−1/y(t))=k·P _{apr}(S _{01} ^{*})·[P(D _{−1}=+1)·P(D _{1}=+1)·P(y(t)/S _{4})+P(D _{−1}=+1)·P(D _{1}=−1)·P(y(t)/S _{5})]+k·P _{apr}(S _{00} ^{*})·[P(D _{−1}=−1)·P(D _{1}=+1)·P(y(t)/S _{6})+P(D _{−1}=−1)·P(D _{1}=−1)·P(y(t)/S _{7})] (18a)
P(D _{0}=−1/y(t))=k·P _{apr}(S _{01} ^{*})·[P(D_{−1}=+1)·{P(D _{1}=+1)·P(y(t)/S _{4})+P(D _{1}=−1)·P(y(t)/S _{5})}]+k·P_{apr}(S _{01} ^{*})·[P(D _{−1}=−1)·{P(D _{1}=+1)·P(y(t)/S _{6})+P(D _{1}=−1)·P(y(t)/S _{7})}] (18b)

[0055]
If the posterior probabilities P(D_{0}=+1/y(t)) and P(D_{0}=−1/y(t)) for the receive information symbol D_{0 }of the target subchannel becoming “0” (=+1) and “1” (=−1) are determined as above, the values are compared or the difference of the logarithm thereof and the threshold value are compared so as to determined the sine (+1 or −1) of the receive information symbol.

[0056]
Decision by Comparing Values

[0057]
Whether the information symbol D_{0 }of the target subchannel is +1 or −1 is decided by computing P(D_{0}=+1/y(t)) and P(D_{0}=−1/y(t)) first, then by using the expressions (19a) and (19 b),
$\begin{array}{cc}\frac{P\left({D}_{0}=+1/y\left(t\right)\right)}{P\left({D}_{0}=1/y\left(t\right)\right)}>1& \left(19a\right)\\ \frac{P\left({D}_{0}=+1/y\left(t\right)\right)}{P\left({D}_{0}=1/y\left(t\right)\right)}<1& \left(19b\right)\end{array}$
and if (19a), then it is decided as D_{0}=+1, and if (19b), then it is decided as D_{0}=−1.

[0058]
Decision by Difference of Logarithm

[0059]
Whether the information symbol D_{0 }of the target subchannel is +1 or −1 is decided by computing ln P(D_{0}=+1/y(t))−ln P(D_{0}=−1/y(t)) (ln is a logarithm with an e base), then deciding the negative/positive of the result. If
ln P(D _{0}=+1/y(t))−ln P(D _{0}=−1/y(t))>0 (19c),
then it is decided as D_{0}=+1, and if
ln P(D _{0}=+1/y(t))−ln P(D _{0}=−1/y(t))<0 (19d),
then it is decided as D_{0}=−1.

[0060]
Since the transmission symbol D
_{0 }is statistically independent (no correlation) and is an equally distributed probability variable, the following expression is established.
$\begin{array}{cc}\{\begin{array}{c}{P}_{\mathrm{apr}}\left({S}_{10}^{*}\right)={P}_{\mathrm{apr}}\left({S}_{00}^{*}\right)={P}_{\mathrm{apr}}\left({S}_{+10}^{*}\right)=1/2\\ {P}_{\mathrm{apr}}\left({S}_{11}^{*}\right)={P}_{\mathrm{apr}}\left({S}_{01}^{*}\right)={P}_{\mathrm{apr}}\left({S}_{+11}^{*}\right)=1/2\end{array}& \left(20\right)\end{array}$
As expression (20) shows, the common multiplier in the expressions (17b) and (18b) does not affect the decision rule, so the expressions (17b) and (18b) become the expressions (21) and (22).
P(
D _{0}=+1
/y(
t))=
P(
D _{−1}=+1)·{
P(
D _{1}=+1)·
P(
y(
t)/
S _{0})+
P(
D _{1}=−1)·
P(
y(
t)/
S _{1})}+
P(
D _{−1}=−1)·{
P(
D _{1}=+1)·
P(
y(
t)/
S _{2})+
P(
D _{1}=−1)·
P(
y(
t)/
S _{3})} (21)
P(
D _{0}=−1
/y(
t))=
P(
D _{−1}=+1)·{
P(
D _{1}=+1)·
P(
y(
t)/
S _{4})+
P(
D _{1}=−1)·
P(
y(
t)/
S _{5})}+
P(
D _{−1}=−1)·{
P(
D _{1}=+1)·
P(
y(
t)/
S _{6})+
P(
D _{1}=−1)·
P(
y(
t)/
S _{7})} (22)
If the expressions (21) and (22) are transformed considering the algebraic sameness of the following expression,
$\begin{array}{cc}\mathrm{ln}\left({e}^{X}+{e}^{Y}\right)=\frac{X+Y}{2}+\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{XY}{2}\right)& \left(a\right)\end{array}$
then the following expressions (23) and (24) are established.
$\begin{array}{cc}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{0}=+1/y\left(t\right)\right)=1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+1/2\xb7\mathrm{ln}\xb7\left\{P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{0}\right)+P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{1}\right)\right\}+1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+1/2\xb7\mathrm{ln}\left\{P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{2}\right)+P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{3}\right)\right\}+\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{\begin{array}{c}\begin{array}{c}1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+1/2\xb7\mathrm{ln}\{P\left({D}_{1}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{0}\right)+P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{1}\right)\}\end{array}\\ \begin{array}{c}1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+1/2\xb7\mathrm{ln}\{P\left({D}_{1}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{2}\right)+P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{3}\right)\}\end{array}\end{array}\right\}& \left(23\right)\\ \mathrm{ln}\text{\hspace{1em}}P\left({D}_{0}=1/y\left(t\right)\right)=1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+1/2\xb7\mathrm{ln}\xb7\left\{P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{4}\right)+P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{5}\right)\right\}+1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+1/2\xb7\mathrm{ln}\left\{P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{6}\right)+P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{7}\right)\right\}+\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{\begin{array}{c}\begin{array}{c}1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+1/2\xb7\mathrm{ln}\{P\left({D}_{1}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{4}\right)+P\left({D}_{1}=1\right)\xb7P\left(y\left(t\right)/{S}_{5}\right)\}\end{array}\\ \begin{array}{c}1/2\xb7\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+1/2\xb7\mathrm{ln}\{P\left({D}_{1}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{6}\right)+P\left({D}_{1}=+1\right)\xb7P\left(y\left(t\right)/{S}_{7}\right)\}\end{array}\end{array}\right\}& \left(24\right)\\ \mathrm{ln}\text{\hspace{1em}}P\left({D}_{0}=+1/y\left(t\right)\right)=\frac{A+B}{2}+\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{AB}{2}\right)& \left(25\right)\\ \mathrm{ln}\text{\hspace{1em}}P\left({D}_{0}=1/y\left(t\right)\right)=\frac{C+D}{2}+\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{CD}{2}\right)& \left(26\right)\end{array}$
Here if the expressions (25) and (26) are used, then A, B, C and D become as follows.
 A=ln P(D_{−1}=+1)+ln {P(D_{1}=+1)·P(y(t)/S_{0})+P(D_{1}=−1)·P(y(t)/S_{1})}
 B=ln P(D_{−1}=−1)+ln {P(D_{1}=+1)·P(y(t)/S_{2})+P(D_{1}=−1)·P(y(t)/S_{3})}
 C=ln P(D_{−1}=+1)+ln {P(D_{1}=+1)·P(y(t)/S_{4})+P(D_{1}=−1)·P(y(t)/S_{5})}
 D=ln P(D_{−1}=−1)+ln {P(D_{1}=+1)·P(y(t)/S_{6})+P(D_{1}=−1)·P(y(t)/S_{7})}

[0065]
If the expressions (25) and (26) are applied to the left side member of the expressions (19c) and (19d), the new decision expression becomes as follows.
$\begin{array}{cc}\mathrm{ln}\text{\hspace{1em}}{D}_{0}=\frac{A+B}{2}\frac{C+D}{2}+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{AB}{2}\right)\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{CD}{2}\right)>/<0& \left(27\right)\end{array}$
By considering the relationship of
$P\left(y\left(t\right)/{S}_{j}\right)=\mathrm{exp}\left\{\frac{1}{{N}_{0}}{\int}_{0}^{T}{\left[y\left(t\right){S}_{j}\right]}^{2}dt\right\}$
acquired by the expression (5) and the expression (4), each term constituting the new decision expression (27) can be rewritten as follows.
Here ln D_{i}=ln P (D_{i}=+1)−ln P (D_{i}=−1).
$\begin{array}{cc}\left(A+B\right)\left(C+D\right)=\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt+{\int}_{0}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)dt+{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt+{\int}_{0}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt\right]+\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)dt\right]\frac{{E}_{0}{E}_{1}}{{N}_{0}}\right\}\right\}\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)dt\right]+\frac{{E}_{0}{E}_{1}}{{N}_{0}}\right\}\right\}+\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt\right]\frac{{E}_{2}{E}_{3}}{{N}_{0}}\right\}\right\}\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt\right]+\frac{{E}_{2}{E}_{3}}{{N}_{0}}\right\}\right\}& \left(28\right)\end{array}$
In the above description, ln D_{i}=lnP(D_{i}=+1/y(t))−lnP(D_{i}=−1/y(t)) is the logarithmic difference of the posterior probabilities of the signal D_{i }transmitted in the ith subchannel being +1 and −1 (soft decision value of the ith subchannel). It is assumed that the energy of the signal S_{j}(t) is E_{j}, and
${E}_{j}={\int}_{0}^{T}{S}_{j}^{2}\left(t\right)dt.$
(AB), (CD) of the expression (27) becomes as follows.
$\begin{array}{cc}\left(AB\right)=\mathrm{ln}\text{\hspace{1em}}{D}_{1}+1/2\xb7\left\{\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt+{\int}_{0}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt\right]\frac{\Delta \text{\hspace{1em}}{E}_{\Sigma}}{{N}_{0}}\right\}+\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)dt\right]\frac{{E}_{0}{E}_{1}}{{N}_{0}}\right\}\right\}\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt\right]+\frac{{E}_{2}{E}_{3}}{{N}_{0}}\right\}\right\}& \left(29\right)\\ \left(CD\right)=\mathrm{ln}\text{\hspace{1em}}{D}_{1}+1/2\xb7\left\{\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt+{\int}_{0}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt\right]+\frac{\Delta \text{\hspace{1em}}{E}_{\Sigma}}{{N}_{0}}\right\}+\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)dt\right]+\frac{{E}_{0}{E}_{1}}{{N}_{0}}\right\}\right\}\text{}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{1/2\xb7\left\{\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{2}{{N}_{0}}\left[{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt{\int}_{0}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt\right]+\frac{{E}_{2}{E}_{3}}{{N}_{0}}\right\}\right\}& \left(30\right)\end{array}$
where
$\begin{array}{cc}\Delta \text{\hspace{1em}}{E}_{\Sigma}=\frac{\left({E}_{0}+{E}_{1}\right)\left({E}_{2}+{E}_{3}\right)}{{N}_{0}}& \left(31\right)\end{array}$
The expressions (27)(30) define the optimum receiver structure of binary signals involving ICI. As the expressions (27)(30) show, the decision information of the adjacent channels is used to decide the sign of the transmission information symbol D of a subchannel. In the decision rule of the expressions (27)(30), ln D_{−1 }and ln D_{+1 }indicate the logarithmic difference of the posterior probability of the information symbol in the lower subchannel (ch−1) and the upper subchannel (ch+1) becoming +1 and the posterior probability of that becoming −1. All calculations are in series, so when processing the data of the target subchannel, the latest posterior probability from the adjacent channels can be used by repeat calculation.

[0066]
As described above, the algorithm is created such that InD_{0}, which is the soft decision target value, is computed by the expressions (27)(30), then “0” or “1” of the receive symbol of the target subchannel is decided depending on the positive/negative of the soft decision target value InD_{0}.

[0000]
(C) Configuration of Receiver

[0067]
FIG. 5 is a block diagram depicting a receiver of a three subchannel model, that is, a receiver based on the maximum posterior probability using ICI (called a turbo receiver), and shows the configuration of only the receive unit of the target subchannel, but the receive units of the other subchannels also have the same configuration. This receive unit also has a configuration to execute the above mentioned algorithm.

[0068]
The receiver 50 of the target subchannel further comprises a correlation unit (can be a match fill) 51, another channel decision result operating unit 52, first and second nonlinear units 53 and 54, and symbol decision unit 55.

[0069]
The multiplier 51 a and integrator 51 b of the correlation unit 51 is a unit for computing
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt$
of the decision expressions (28)(30), the multiplier 51 c and integrator 51 d are units for computing
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{1}\left(t\right)\text{\hspace{1em}}dt,$
the multiplier 51 e and integrator 51 f are units for computing
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt,$
and the multiplier 51 g and integrator 51 h are units for computing
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{3}\left(t\right)dt.$
The addition unit 51 i adds the integration output of the integrators 51 b and 51 d, subtractor 51 j subtracts the integration outputs of the integrators 51 b and 51 d, the addition unit 51 k adds the integration outputs of the integrators 51 f and 51 h, and the subtractor 51 m subtracts the integration outputs of the integrators 51 f and 51 h. The addition unit 51 n adds the outputs of the addition units 51 i and 51 k, and outputs the first term of the right side member of the expression (28), that is
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt+\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{1}\left(t\right)dt+\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{2}\left(t\right)dt+\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{3}\left(t\right))dt$
The subtraction unit 51 _{p }subtracts the outputs of the addition units 51 i and 51 k, and outputs
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt+\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{1}\left(t\right)dt\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{2}\left(t\right)dt\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{3}\left(t\right))dt$
The division units 51 q and 51 r divide the input signal ½, and output the result.

[0070]
The other channel decision result operating unit 52 comprises the adders 52 a52 c, which compute the following respectively.
$\mathrm{ln}\text{\hspace{1em}}{D}_{+1}+\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{1}\left(t\right)dt,\text{}\mathrm{ln}\text{\hspace{1em}}{D}_{+1}+\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt\frac{2}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{3}\left(t\right)dt,\text{}\mathrm{ln}\text{\hspace{1em}}{D}_{1}+\frac{1}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt+\frac{1}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{1}\left(t\right)dt\frac{1}{{N}_{0}}{\int}_{0}^{T}y\left(t\right)\xb7{S}_{2}\left(t\right)dt\frac{1}{{N}_{0}}{\int}_{0}^{T}y\left(t\right){S}_{3}\left(t\right))dt$

[0071]
The first nonlinear unit 53 is a unit for computing ln cosh of the secondfifth terms of the right side member of the expression (28), and comprises the first and second nonlinear sections 53 a and 53 b. The addition units 71 a and 71 b of the first nonlinear section 53 a compute the content of { } of the second and third terms of the right side member of the expression (28) respectively. Here the (E_{0}−E_{1})/N_{0}=ΔE_{1}. ln cosh computing units 71 c and 71 d compute the second and third terms of the right side member of the expression (28) respectively, and the subtractor 71 e subtracts the computing result of the ln cosh computing unit 71 d from the computing result of the ln cosh computing unit 71 c.

[0072]
The addition units 71 a′ and 71 b′ of the second nonlinear unit 53 b compute the content of { } of the fourth and fifth terms of the right side member of the expression (28) respectively. Here the (E_{2}−E_{3})/N, =ΔE_{2 }ln cosh computing units 71 c′ and 71 d′ compute the fourth and fifth terms of the right side member of the expression (28) respectively, and the subtractor 71 e′ subtracts the computing result of the in cosh computing unit 71 d′ from the computing result of the in cosh computing unit 71 c′, and outputs the result.

[0073]
The addition unit 53 c synthesizes the outputs of the adders 71 e and 71 e′ and the division unit 53 d divides the synthesized signal by ½, and outputs the computing results of the secondfifth terms of the expression (28).

[0074]
The second nonlinear unit 54 is a unit for computing the firstthird terms of the right side member of the expressions (29) and (30). The addition units 54 a and 54 b compute the first term of the right side member of the expressions (29) and (30) respectively, the addition units 54 c and 54 d compute the second term and third term of the right side member of the expressions (29) and (30) respectively, the addition units 54 e and 54 f compute the right side member of the expressions (29) and (30) respectively, ln cosh computing units 54 g and 54 h compute ln cosh
$\frac{AB}{2}\text{\hspace{1em}}\mathrm{and}\text{\hspace{1em}}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\text{\hspace{1em}}\frac{CD}{2}$
respectively, and the subtraction unit 54 i computes the difference between the outputs of the ln cosh computing units 54 g and 54 h, and outputs
$\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\text{\hspace{1em}}\frac{AB}{2}\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\text{\hspace{1em}}\frac{CD}{2}.$

[0075]
The adder 55 a of the symbol decision unit 55 adds the output signal of the division unit 51 r of the correlation unit 51 and the output signal of the nonlinear unit 53, and outputs
$\frac{AB}{2}\frac{CD}{2},$
and the addition unit 55 b generates the InD_{0 }(soft decision target value) of the expression (27). The decision unit 55 c decides whether InD_{0 }is positive or negative, and decides that the receive symbol is “0 ” if positive, and that it is −1′ if negative. The symbol decision unit 55 feeds back the computing result (soft decision target value) InD_{0 }of the expression (27) to the other channel decision result operating units of the receive units 40 and 60 of the lower and upper adjacent subchannels.
(D) General Configuration Example of Communication System of Present Invention Having Four SubChannels

[0076]
FIG. 6 is a general block diagram depicting a communication system for demodulating receive data using the interference between lower one subchannel and upper two subchannels, comprising four transmitters 121, 122, 123 and 124 for transmitting data independently via four subchannels, ch−1, ch0, ch+1 and ch+2, many crosstalk paths 131 _{ij }having the coupling coefficient α_{ij }from the ith subchannel to the jth subchannel, four receivers 150, 160, 170 and 180 which are installed for each subchannel for receiving data from the corresponding subchannel and performing soft decision for the receive data, and means 191 and 192 for inputting the soft decision target value of each receiver to the receiver 160 of the target channel ch0. Means for inputting the other receivers is omitted in FIG. 6, but can be regarded as the same for the receiver 160. 132139 and 140143 are synthesizing units for synthesizing ICI signals and noises.

[0077]
The receiver 160 of the subchannel ch0 adjusts its own soft decision target value using the soft decision target values which were input from the receivers 150, 170 and 180 of the lower and upper subchannels ch−1, ch+1 and ch+2, and decides “0” or “1” of the receive data based on the soft decision target value. In the same way, the other receivers as well adjust their own soft decision target values using the soft decision target values which were input from the receivers of the lower and upper subchannels, and decides “0” or “1” of the receive data based on the adjusted soft decision target values.

[0000]
(E) Receive Symbol Demodulation Algorithm in Four SubChannels

[0078]
An algorithm for the receiver of the target subchannel ch0 to demodulate the receive symbol in the communication system shown in FIG. 6 will be described.

[0079]
The principle of the demodulation algorithm is deriving the value InD_{0}, which indicates the difference between the posterior probability P (D_{0}=+1/y(t)) of the information symbol received by the target subchannel ch0 being “0” (=+1) and the posterior probability P (D_{0}=−1/y(t)) of the information symbol being “1” (=−1), just like the case of the three subchannel model. Since the probability difference InD_{0 }of the target subchannel is the difference between the posterior probability P(D_{0}=+1/y(t)) of the receive information symbol being “0” (=+1) and the posterior probability P(D_{0}=−1/y(t)) of the receive information symbol being “1” (=−1), the receive information of the target subchannel can be decided as “0” if ln D_{0}>0, and the receive information of the target subchannel is “1” if ln D_{0}<0.

[0080]
It is assumed that binary information is transmitted as signal S*
_{ij}(t) via two adjacent subchannels. The index i in S*
_{ij}(t) indicates the subchannel number, and the index j is determined by the sign of the information symbol D
_{i}(i=−1, 0 or 1) in the subchannel i. In other words,
 if D_{i}=+1, then j=0
 if D_{i}=−1, then j=1
Hereafter to simplify notation, the time dependency of S*_{ij}(t) in expressions is omitted. In other words, S*_{ij}(t) is denoted as S*_{ij}.

[0083]
As FIG. 6 shows, the signal of the target subchannel affected by ICI from the lower and upper subchannels is expressed as the linear coupling of the signals S*_{−1j}, S*_{1j }and S*_{2j }transmitted by the upper and lower subchannels, and the target channel signal S*_{0j }by the crosstalk coefficient α. The crosstalk coefficient α is a value according to the leak of crosstalk. If the information symbol D_{0 }of the target channel is +1, then the receive signal S_{j }(j=0−7) of the target channel becomes
$\begin{array}{cc}\{\begin{array}{c}{S}_{0}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=+1,{D}_{2}=+1\\ \begin{array}{c}{S}_{1}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=+1,{D}_{2}=1\end{array}\\ \begin{array}{c}{S}_{2}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=1,{D}_{2}=+1\end{array}\\ \begin{array}{c}{S}_{3}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=+1,{D}_{1}=1,{D}_{2}=1\end{array}\end{array}\text{}\{\begin{array}{c}{S}_{4}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=+1,{D}_{2}=+1\\ \begin{array}{c}{S}_{5}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=+1,{D}_{2}=1\end{array}\\ \begin{array}{c}{S}_{6}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=1,{D}_{2}=+1\end{array}\\ \begin{array}{c}{S}_{7}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=+1,{D}_{1}=1,{D}_{1}=1,{D}_{2}=1\end{array}\end{array}& \left(32\right)\end{array}$
depending on whether the signals D_{−1}, D_{1 }and D_{2 }of the lower and upper subchannels are +1 or −1.
j of the signal S_{j }indicates the signal number. In the same way, if the information symbol D_{0 }of the target channel is −1, then the receive signal S_{j }(j=8−15) of the target channel becomes
$\begin{array}{cc}\{\begin{array}{c}{S}_{8}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=+1,{D}_{1}=+1,{D}_{2}=+1\\ \begin{array}{c}{S}_{9}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=+1,{D}_{1}=+1,{D}_{2}=1\end{array}\\ \begin{array}{c}{S}_{10}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=+1,{D}_{1}=1,{D}_{2}=+1\end{array}\\ \begin{array}{c}{S}_{11}={S}_{00}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=+1,{D}_{1}=1,{D}_{2}=1\end{array}\end{array}\text{}\{\begin{array}{c}{S}_{12}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=1,{D}_{1}=+1,{D}_{2}=+1\\ \begin{array}{c}{S}_{13}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=1,{D}_{1}=+1,{D}_{2}=1\end{array}\\ \begin{array}{c}{S}_{14}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}+{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=1,{D}_{1}=1,{D}_{2}=+1\end{array}\\ \begin{array}{c}{S}_{15}={S}_{00}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{10}\xb7{S}_{10}^{*}{\alpha}_{20}\xb7\\ {S}_{20}^{*},{D}_{0}=1,{D}_{1}=1,{D}_{1}=1,{D}_{2}=1\end{array}\end{array}& \left(33\right)\end{array}$
depending on whether the signals D_{−1}, D_{1 }and D_{2 }of the lower and upper subchannels area +1 or −1.

[0084]
After introducing ICI, S_{j }(j=0, 1, 2, . . . 15) is used as 16 signals at the input of the receiver of each subchannel. The index j of S_{j }in the expressions (32) and (33) indicates the signal number, and is determined by pairing the symbols D_{−1}, D_{1}, D_{2 }and D_{0 }in the lower subchannel, upper subchannel and target subchannel.

[0085]
By considering the following [1] and [2], the algorithm for optimum reception can be further developed. In other words, by considering [1] that the signs of some information signals are the opposite, that is S*_{−10}=−S*_{−11}, S*_{00}=−S*_{01}, S*_{10}=−S*_{11}, and S*_{−20}=−S*_{21}, and [2] to transmit information signals a same signal is used for the lower, upper and target subchannels, that is, S*_{−10}=S*_{00}=S*_{10}=S*_{20 }and S*_{−11}=S*_{01}=S*_{11}=S*_{21}, the algorithm for optimum reception can be further developed. The latter [2] indicates that all the subchannels have the same value and the information signals of all the subchannels have no difference in amplitude, waveform and energy. In this case, the signals of the expressions (32) and (33) in each subchannel become a pair, having opposite signs, as shown in the following expressions.
S_{0}=−S_{15}, S_{1}=−S_{14}, S_{2}=−S_{13}, S_{3}=−S_{12 }S_{4}=−S_{11}, S_{5}=−S_{10}, S_{6}=−S_{9}, S_{7}=−S_{8} (34)

[0086]
Hereafter this case can be considered in the same way as the three subchannel model. In other words, just like the case of the three subchannel model, the posterior probabilities P(D
_{0}=+1/y(t)) and P(D
_{0}=−1/y(t)) of the receive information symbol D
_{0 }of the target subchannel becoming “0” (=+1) and “1” (=−1) are determined. If these are determined, the sign (+1 or −1) of the receive symbol can be determined by comparing these values or comparing the difference of the logarithms thereof and the threshold value. In other words, to determine whether the information symbol D
_{0 }of the target subchannel is +1 or −1,
$\frac{P\left({D}_{0}=+1/y\left(t\right)\right)}{P\left({D}_{0}=1/y\left(t\right)\right)}$
is computed first and compared with 1, and if the result is greater than 1, it is decided that D
_{0}=+1, and if the result is smaller than 1, it is decided that

 ln P(D_{0}=+1/y(t))−ln P(D_{0}=−1/y(t)) is computed and then the negative or positive of the result is decided. In other words, if positive it is decided that D_{0}=+1, and if negative it is decided that D_{0}=−1. y(t) is a synthesized signal (y(t)=S_{j}+n(t)) of the signal series S_{j }involving ICI and the white Gaussian noise n (t) having spectrum power intensity N_{0}.

[0088]
In the case of a four subchannel model,
$\begin{array}{cc}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{0}=+1/y\left(t\right)\right)=\frac{a+b}{2}+\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{ab}{2}\right)& \left(35\right)\\ \mathrm{ln}\text{\hspace{1em}}P\left({D}_{0}=1/y\left(t\right)\right)=\frac{c+d}{2}+\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{cd}{2}\right)& \left(36\right)\end{array}$
Here a, b, c and d are as shown in the following expressions.
$\begin{array}{cc}a=\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+0.5\left\{\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{0}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{1}\right))+\\ \begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{2}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{3}\right))\end{array}\end{array}\right\}+\text{}\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{0.5\xb7\left\{\begin{array}{c}\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\\ \mathrm{ln}\text{\hspace{1em}}\{P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{0}\right)+\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{1}\right)\}\end{array}\\ \mathrm{ln}\left(P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{2}\right)+\right\}\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{3}\right)\end{array}\right\}\right\}& \left(37\right)\\ b=\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+0.5\left\{\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{4}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{5}\right))+\\ \begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{6}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{7}\right))\end{array}\end{array}\right\}+\text{}\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{0.5\xb7\left\{\begin{array}{c}\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\\ \mathrm{ln}\text{\hspace{1em}}\{P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{4}\right)+\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{5}\right)\}\end{array}\\ \mathrm{ln}\{P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{6}\right)+\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{7}\right)\}\end{array}\right\}\right\}& \left(38\right)\\ c=\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+0.5\left\{\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{8}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{9}\right))+\\ \begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{10}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{11}\right))\end{array}\end{array}\right\}+\text{}\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{0.5\xb7\left\{\begin{array}{c}\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\\ \mathrm{ln}\text{\hspace{1em}}\{P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{8}\right)+\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{9}\right)\}\end{array}\\ \mathrm{ln}\{P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{10}\right)+\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{11}\right)\}\end{array}\right\}\right\}& \left(39\right)\\ c=\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+0.5\left\{\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{12}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{13}\right))+\\ \begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\mathrm{ln}(P\left({D}_{2}=+1\right)\xb7\\ P\left(y\left(t\right)/{S}_{14}\right)+P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{15}\right))\end{array}\end{array}\right\}+\text{}\mathrm{ln}\text{\hspace{1em}}2+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left\{0.5\xb7\left\{\begin{array}{c}\begin{array}{c}\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=+1\right)\mathrm{ln}\text{\hspace{1em}}P\left({D}_{1}=1\right)+\\ \mathrm{ln}\text{\hspace{1em}}\{P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{12}\right)+\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{13}\right)\}\end{array}\\ \mathrm{ln}\{P\left({D}_{2}=+1\right)\xb7P\left(y\left(t\right)/{S}_{14}\right)+\\ P\left({D}_{2}=1\right)\xb7P\left(y\left(t\right)/{S}_{15}\right)\}\end{array}\right\}\right\}& \left(40\right)\end{array}$

[0089]
Finally ln D_{0 }is given by the following expression using the expressions (35) and (36).
$\begin{array}{cc}\mathrm{ln}\text{\hspace{1em}}{D}_{0}=\frac{a+b}{2}\frac{c+d}{2}+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\text{\hspace{1em}}\left(\frac{ab}{2}\right)\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{cd}{2}\right)& \left(41\right)\end{array}$
(F) Receiver of the Present Invention

[0090]
FIG. 7 and FIG. 8 are block diagrams depicting a receiver of the target subchannel of the present invention in the case when the crosstalk from upper two subchannels and lower one subchannel exist, which are separated in the figures by a dash and dotted line, and implements the computation of the right side member of the expression (41). FIG. 7 shows the configuration of the left side of the receiver, and FIG. 8 shows the right side thereof. If the receiver in FIG. 7 and FIG. 8 is the receiver of the target channel ch0, this receiver has a configuration combining the receiver of the three subchannel model which receives crosstalk from the channels ch+1 and ch+2, and the receiver of the two subchannel model which receives crosstalk from the channel ch1, and the expression (41) becomes the sum of the values at the points P1, P2 and P3 in FIG. 7 and FIG. 8.

[0091]
The receiver 160 of the target subchannel comprises a correlation unit 161, firstthird computing units 162164, synthesizing unit 165 and decision unit 166. In the figures, ∫dt is an integrator for computing
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{i}\left(t\right)dt.$
lnD_{i}=lnP(D_{i}=+1)−lnP(D_{i}=−1) is the logarithmic difference of the posterior probabilities of the signal Di transmitted by the ith subchannel (i=−1, +1, +2) becoming +1 or −1 (soft decision value in the ith subchannel). Here the energy of the signal S_{j}(t) is E_{j}, which is given by
${E}_{j}={\int}_{0}^{T}{S}_{j}^{2}\left(t\right)dt.$
Also
$\Delta \text{\hspace{1em}}{E}_{\Sigma}=\frac{{E}_{0}+{E}_{1}{E}_{2}{E}_{3}}{{N}_{0}},\text{}\Delta \text{\hspace{1em}}{E}_{\Sigma}=\frac{{E}_{4}+{E}_{5}{E}_{6}{E}_{7}}{{N}_{0}},\text{}\Delta \text{\hspace{1em}}{E}_{\Sigma}=\frac{{E}_{0}+{E}_{1}+{E}_{2}+{E}_{3}{E}_{4}{E}_{5}{E}_{6}{E}_{7}}{{N}_{0}}$
$\Delta \text{\hspace{1em}}{E}_{0}=\frac{{E}_{0}{E}_{1}}{{N}_{0}},\Delta \text{\hspace{1em}}{E}_{2}=\frac{{E}_{2}{E}_{3}}{{N}_{0}},\text{}\Delta \text{\hspace{1em}}{E}_{4}=\frac{{E}_{4}{E}_{5}}{{N}_{0}},\Delta \text{\hspace{1em}}{E}_{6}=\frac{{E}_{6}{E}_{7}}{{N}_{0}}$

[0092]
The correlation unit 161 is comprised of the computing units (multiplier and integrator) for computing
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt~\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{7}\left(t\right)dt$
and the addition/subtraction circuit for computing S_{0}′+S_{1}′, S_{0}′−S_{1}′, S_{2}′+S_{3}′, S_{2}′−S_{3}′ . . . ΣS_{j}′ (j=0−7) when
$\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{0}\left(t\right)dt~\frac{2}{{N}_{0}}{\int}_{o}^{T}y\left(t\right)\xb7{S}_{7}\left(t\right)dt$
are expressed as S_{0}′, S_{1}′, S_{7}′ respectively.

[0093]
The first computing unit 162 has a configuration the same as the configuration enclosed by a dash and dotted line in FIG. 5, and computes the secondfifth terms of the right side member of the expression (28) and expressions (29) and (30) for the signals S_{0}(t), . . . S_{3}(t) out of the signals S_{0}(t), S_{1}(t), . . . S_{7}(t). In the addition unit 165 a of the synthesizing unit 165, the first term of the right side member (=S_{0}′+S_{1}′+S_{2}′+S_{3}′) of the expression (28) is added, and computation of the expression (29) completes.

[0094]
The second computing unit 163 has the same configuration as the configuration enclosed by the dash and dotted line in FIG. 5, and computes the second to fifth terms of the right side member of the expression (28) and the expressions (29) and (30) for the signals S_{4}(t), . . . S_{7}(t) out of the signals S_{0}(t), S_{1}(t), . . . S_{7}(t). However in the expressions (28), (29) and (30), S_{0}(t) . . . S_{3}(t) are replaced with S_{4}(t) . . . S_{7}(t). In the addition unit 165 a of the synthesizing unit 165, the first term of the right side member(=S_{4}′+S_{5}′+S_{6}′+S_{7}′) of the expression (28) is added, and computation for the expression (29) completes.

[0095]
The synthesizing unit 165 synthesizes the computing result of the right side member of the expression (27) for the signals S_{0}(t) . . . S_{3}(t), that is
$\begin{array}{cc}\frac{A+B}{2}\frac{C+D}{2}+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{AB}{2}\right)\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{CD}{2}\right)& \left(42\right)\end{array}$
and the computing result of the right side member of the expression (27) for the signals S_{4}(t) . . . S_{7}(t), that is
$\begin{array}{cc}\frac{{A}^{\prime}+{B}^{\prime}}{2}\frac{{C}^{\prime}+{D}^{\prime}}{2}+\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{{A}^{\prime}{B}^{\prime}}{2}\right)\mathrm{ln}\text{\hspace{1em}}\mathrm{cosh}\left(\frac{{C}^{\prime}{D}^{\prime}}{2}\right)& \left(43\right)\end{array}$
and adds the computing result of the third computing unit 164 to the synthesized result (value at the point P1 in the figure), and inputs it to the decision unit 166 as ln D_{0 }of the expression (41).

[0096]
The third computing unit 164 corrects the computing result based on the soft decision data ln D_{−1 }of the lower subchannel ch−1, and performs predetermined computation on the correction result, and inputs it to the synthesizing unit 165.

[0097]
If the values of the firstfifth terms of the expression (28) for the signals S_{0}(t), S_{1}(t), S_{2}(t) and S_{3}(t) are expressed as {circle over (1)}{circle over (5)}, the values of the firstfifth terms of the expression (28) for the signals S_{4}(t) S_{5}(t), S_{6}(t) and S_{7}(t) are expressed as {circle over (1)}′{circle over (5)}′, and the output of the soft decision data ln D_{−1 }operating unit 164 a is expressed as {circle over (6)}, then the value of the point P2 becomes
ln cosh(½)·[{({circle over (2)}+{circle over (4)}−{circle over (2)}′−{circle over (4)}′)/2+{circle over (6)}−ΔΣ_{Σ}}+ln cosh {(A−B)/2}−ln cosh{(A′−B′)/2}] (44)
and the value of the point P3 becomes
ln cosh(½)·[{{circle over (3)}′+{circle over (5)}′−{circle over (3)}−{circle over (5)})/2+{circle over (6)}+ΔΣ_{Σ}}+ln cosh {(C′−D′)/2}−ln cosh{(C−D)/2}] (45)
Therefore ln D_{0 }(soft decision target value) after synthesizing the values of the points P1, P2 and P3, that is ln D_{0 }(soft decision target value) given by the expression (41) is input to the symbol decision unit 166. Here ln D_{0}=(42)+(43)+(44)+(45).

[0098]
The symbol decision unit 166 decides the positive/negative of the ln D_{0 }(soft decision target value), and if positive the receive symbol is decided as “0”, and if negative it is decided as “1”. Also the symbol decision unit 166 feeds back the in D_{0 }(soft decision target value) to the decision result operating unit of the receive units 150, 170 and 180 of the lower and upper subchannels.

[0099]
As described above, in the multicarrier communication system for transmitting/receiving signals via at least four subchannels, the receiver of the target subchannel ch0 adjusts its own bit decision target value ln D_{0 }using the soft decision target values ln D_{+1}, ln D_{+2 }and ln D_{−1}, in the subchannels other than the target subchannel, and decides the receive data based on this soft decision target value.

[0000]
(G) Similarity with a Turbo Decoder

[0100]
The above mentioned demodulation algorithm of the receive data of the present invention is similar to the turbo decoder of the turbo codes written in the following document.

[0101]
Document: M. C. Valenti and B. D. Woerner: “Variable latency turbo codes for wireless multimedia applications”, Proc. Int. Symposium on Turbo codes and Related Topics, Brest, France, September 1997, pp. 216219.

[0102]
Because of the similarity with the turbo decoder, let us call the algorithm of the present invention a ‘turbo receiver’. In the turbo decoder, each decoder transfers the information to the other decoders, and refines the estimated posterior probability sequentially using the information derived by the other decoders. In the same way, in the algorithm of the present invention as well, the information derived from one subchannel is used to refine the estimated posterior probability of the other channel after nonlinear processing, and the information derived from the latter subchannel is used to refine the estimated posterior probability of the former channel. If an individual decoder output is hard bit decision (hard decision) format in the turbo decoder, sharing information has few advantages. A hard bit decision is similar to the decision feedback equalizer proposed by Viterbo and Fazel in the above mentioned Document 2 for canceling ICI. Here the hard bit decision is executed only at the end of a repeat.

[0103]
This structural similarity is because of the following reasons. In other words, in the turbo receiver, just like the case of turbo codes, the same information is transmitted on the subchannel having unrelated noise due to the presence of ICI. Depending on the behavior of this unrelated noise, the estimation (or the reliability of the decision of) posterior probability can be improved using the estimated posterior probability derived from other subchannels.

[0104]
Just like the case of the repeat turbo decoder, the algorithm of the present invention performs one or more repeats before the final decision for the received information. If the data is an equally distributed probability variable at the first step, that is when a decision from other channels cannot be used,
P(D _{−1}=+1)=½, P(D _{−1}=−1)=½
P(D _{+1}=+1)=½, P(D _{+1}=−1)=½
P(D _{+2}=+1)=½, P(D _{+2}=−1)=½
can be set for the first subchannel. This setting is the best. Therefore in the first step, the difference ln D_{−1 }of the posterior probabilities in the low subchannel ch−1 is regarded as 0. According to the same concept, in the upper subchannels ch+1 and ch+2, the difference of the posterior probabilities is regarded as ln D_{+1}=0 and ln D_{+2}=0. By calculating the expressions (35)(36) and (41), assuming ln D_{−1}=ln D_{1}=ln D_{2}=0. the first estimate of ln D_{0}, which was unknown, can be acquired. In the same way, in an N subchannel communication system, the lower subchannel computes ln D_{−1 }assuming ln D_{−2}=ln D_{0}=ln D_{1}=0, and the upper subchannel computes ln D_{1 }assuming ln D_{3}=ln D_{2}=ln D_{0}=0 at the first repeat according to the algorithm of the present invention. In the second step, ln D_{−1}, ln D_{1 }and ln D_{2 }acquired in the previous step are applied to the decision expressions (35)(36) and (41) to compute the new estimate value of the posterior probability of the target subchannel. By this, the output of one subchannel receiver is used as the prior probability for the other receivers.

[0105]
FIG. 9 shows the constellation of the target channel in the communication system where N=64, and is a case when QPSK modulation with the S/N ratio=20 dB is performed after a different number of times of repeats. The cross channel leak coefficient here is α_{−10}=0.25, α_{10}=0.15 and α_{20}=0.075. (A) is QPSK modulated original data, (B) are signals deteriorated by ICI, (C) is a receive signal with an S/N ratio=20 dB, (D) is the receive data after one repeat according to the present invention, and (E) is the constellation of the receive data after the second repeat according to the present invention.

[0106]
As shown here, according to the present invention, the dispersion in constellation is small, and the BER is improved to become smaller. As the number of repeats increases, the dispersion in constellation decreases further, and BER is further improved.

[0000]
(H) Noise Immunity and Simulation Results

[0107]
In order to prove the validity of the nonlinear signal processing of the present invention, computer simulation was performed for the receiver of the present invention and conventional matched filter receiver. FIG. 10 shows the average BER performance in the receiver of the present invention, and the matched filter receiver as a function of 2Eb/N_{0 }in the case of α_{−10}=0.25, α_{10}=0.15 and α_{20}=0.075 (see simulation results AD). Eb/N_{0 }is a ratio of the average receive signal energy Eb against the background noise power spectrum intensity N_{0 }per bit. As a reference, the simulation result E of the receiver of the present invention in the case of α_{−1}=α_{10}=α_{20}=0 without ICI (equivalent to the matched filter receiver), is shown in FIG. 9. Also as a reference, the BER simulation result F of the matched filter receiver when ICI does not exist, which was calculated using the expression (46), is shown.
$\begin{array}{cc}{P}_{\mathrm{err}}=\frac{1}{2}\xb7\mathrm{erfc}\text{(}\sqrt{0.5\xb7\mathrm{SNR}}& \left(46\right)\end{array}$
where erfc
$\left(x\right)=\mathrm{erfc}\left(x\right)=1\mathrm{erf}\left(x\right)=\frac{2}{\sqrt{\pi}}{\int}_{x}^{\infty}{e}^{{t}^{2}}dt$

[0108]
The BER performance acquired by computer simulation and the BER performance calculated using the expression (46) match well. As the plot in FIG. 10 shows, the BER of the receiver of the present invention is not different from the BER of the conventional matched filter base receiver acquired using the expression (46) if ICI does not exist. The latter BER is indicated as “Reference” (E) in FIG. 10. When ICI exists (in the case of α_{01}=0.25, α_{01}=0.15 and α_{20}=0.075), the performance of the conventional device (repeat once, characteristic A), which does not perform nonlinear processing, is not as good as the receiver of the present invention, and this is particularly obvious in a high Eb/N_{0}, as the simulation results shows.

[0000]
(I) Application to DMT System

[0109]
As an application of the turbo receiver of the present invention, a DMT base communication system is considered. FIG. 11 is a block diagram depicting the DMT base communication system using this turbo receiver, and has a configuration where the turbo receiver of the present invention is disposed in the subsequent stage of the FFT section of the receiver in a known DMT communication system.

[0110]
In the communication system in FIG. 11, the input beam stream with data rate R (bits/sec: bps) is transferred at the new rate R/N (bps) after the serialparallel converter (S/P) 201 through N number of parallel subchannels. The N point IFFT 202 combines the N parallel data and converts it into one set of realtime domain sample signals. In the parallelserial converter (P/S) 203, these N samples are converted into a serial format, and are continuously input into the digitalanalog converter (DAC) 204. The output signal of the low pass filter (LPF) 205 at the DAC output side is the duration DMT signal. In the white Gaussian noise channel, the transmission DMT signal is deteriorated by the white Gaussian noise n(t) and is sent to the DMT receiver 300. The receiver executes a function the opposite of the transmitter. The FFT 301 performs demodulation processing for the signals sent via each subchannel as N matched filter arrays. The turbo 302 _{1}302 _{N }perform subchannel processing based on the turbo algorithm of the present invention, and by this, BER improves even if a frequency offset exists. 303 is the AD converter, 304 is the serialparallel converter and 305 is the parallelserial converter.

[0111]
FIG. 12 shows the BER performance of a conventional DMT base receiver and the BER performance of a DMT receiver which has the turbo processing function of the present invention, and performs three times and six times of turbo repeats. In FIG. 12, a case of N=64 is shown, and the BER performance is shown for 2Eb/N_{0 }using a frequency offset normalized by an interchannel frequency as a parameter, and “proposed” is indicated by the BER characteristic B and B′ (ICIfour model) of the present invention.

[0112]
As FIG. 12 shows, the BER characteristic improves as the frequency offset becomes smaller, and the BER characteristic is better in the “ICIfour model” of the present invention than the conventional device. In the case of the proposed “ICIthree model” (characteristics A and A′), the BER characteristic improves for 2 dB.

[0113]
As described above in the multicarrier communication system, the effect of ICI on adjacent subchannels was studied. The performance of a conventional matched filter receiver rapidly deteriorates as the coupling of adjacent subchannels increase or as the frequency offset increases. Whereas the present invention is a receiver based on an estimated posterior probability, and a receiver of each subchannel is a turbo receiver for transferring information to the receivers of the adjacent subchannels, and refines the estimated posterior probability using the information derived by the receivers of the adjacent subchannels repeatedly. Therefore the turbo receiver of the present invention can improve BER performance considerably compared with a conventional matched filter receiver. This is because the nonlinear signal processing of the turbo algorithm of the present invention uses the information acquired by the adjacent subchannels so as to maximize the posterior probability. The biggest improvement in BER is generated in a high S/N ratio area where ICI dominates Gaussian noise. According to the simulation results, the turbo receiver of the present invention can achieve good performance throughout a considerably wide rage of ICI coupling coefficients.